The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer's specifications that the standard deviation of the amount of paint is 0.009 gallon. You select a random sample of 55 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon. Complete parts (a) through (e) below. Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a = 0.01.) Let u be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H,. Ho: H = 1.0 H u t 10
The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer's specifications that the standard deviation of the amount of paint is 0.009 gallon. You select a random sample of 55 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon. Complete parts (a) through (e) below. Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a = 0.01.) Let u be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H,. Ho: H = 1.0 H u t 10
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
please answer for what is the final conclusion?
Also answer questions below.
B) Compute the P value and interpret its meaning.
P Value=
Interpret the meaning of the P value.
Multiple choice answers for interpreting p value are same as options for final conclusion that are in the picture below.
C) Construct a 95% confidence interval estimate of the population mean amount of paint.
__
![**Assessing the Mean Amount of Paint in 1-Gallon Cans**
The manager of a paint supply store aims to determine if there is a significant difference in the mean amount of paint contained in 1-gallon cans from a well-known manufacturer, where the expected mean is 1 gallon. The standard deviation according to the manufacturer is 0.009 gallons. A sample of 55 cans was selected, with a measured mean of 0.995 gallons.
**Objective:**
Determine if the mean amount of paint differs from 1.0 gallon using a significance level of α = 0.01.
**Hypotheses:**
- Null Hypothesis (H₀): µ = 1.0
- Alternative Hypothesis (H₁): µ ≠ 1.0
**Test Statistic:**
\[ Z_{\text{STAT}} = -4.12 \]
(Rounded to two decimal places)
**Critical Values:**
- Critical values are -2.58 and 2.58 for α = 0.01
(Rounded to two decimal places.)
**Conclusion:**
- Option D: Reject H₀. There is sufficient evidence that the mean amount is different from 1.0 gallon.
The analysis indicates a statistically significant difference from the hypothesized mean of 1 gallon, suggesting the manufacturer's specification may not reflect the actual content.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4face5cd-9945-4486-9997-75d61face8c6%2F588c6f62-e522-4435-bcbd-ff7a34f56c48%2Frnzg2e9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Assessing the Mean Amount of Paint in 1-Gallon Cans**
The manager of a paint supply store aims to determine if there is a significant difference in the mean amount of paint contained in 1-gallon cans from a well-known manufacturer, where the expected mean is 1 gallon. The standard deviation according to the manufacturer is 0.009 gallons. A sample of 55 cans was selected, with a measured mean of 0.995 gallons.
**Objective:**
Determine if the mean amount of paint differs from 1.0 gallon using a significance level of α = 0.01.
**Hypotheses:**
- Null Hypothesis (H₀): µ = 1.0
- Alternative Hypothesis (H₁): µ ≠ 1.0
**Test Statistic:**
\[ Z_{\text{STAT}} = -4.12 \]
(Rounded to two decimal places)
**Critical Values:**
- Critical values are -2.58 and 2.58 for α = 0.01
(Rounded to two decimal places.)
**Conclusion:**
- Option D: Reject H₀. There is sufficient evidence that the mean amount is different from 1.0 gallon.
The analysis indicates a statistically significant difference from the hypothesized mean of 1 gallon, suggesting the manufacturer's specification may not reflect the actual content.
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